Meriam, Kraige & Bolton — Statics of Particles: Problem 2_112

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/112 Determine the moment associated with the pair of 400-N forces applied to the T-shaped structure. Problem 2/112 1. Analysis of the Force System The problem shows a T-shaped structure fixed at the origin . Two equal and opposite forces of magnitude are applied at points and at the ends of the cross- bar. These two forces constitute a couple. The moment of a couple is the same about any point in space and is calculated as the cross product of the position vector between the application points and one of the forces. From the diagram, we establish a right-handed coordinate system: The x-axis lies along the stem of the T-structure, from toward the junction. The y-axis is the vertical axis. The z-axis lies along the cross-bar, pointing from the junction toward point . Based on the given dimensions: The stem has a length of . Point is located at from the junction along the positive z-axis. Position vector . Point is located at from the junction along the negative z-axis. Position vector . The vector from point to point is: 2. Vector Expression for the Forces The forces are applied in planes parallel to the - plane at an angle of with the vertical (-axis). Looking at the arrows in the diagram: O F=400 NAB O A 0.45 m A0.25 m r = A 0.45i+0.25k m B0.25 m r = B 0.45i−0.25k m BA r = BA r − A r = B (0.45i+0.25k)−(0.45i−0.25k)=0.5k m xy15 ∘ y The force at () points away from the wall (positive direction) and downward (negative direction): T